R.C.
I am a mother of three girls 15, 14 and 12 years old. Kids that are two should either be completely ignored when they are throwing a fit, or should be removed to another room to throw their fit, and told can come back when they are done. Removing them sometimes becomes a battle in and of itself so I recommend completely ignoring them. But that means completely and by everyone in the room that knows them.
I would explain this to your in-laws and tell them that you are trying to help your child get over this stage as soon as possible and ask for their help. Tell them that you want them to completely ignore your child when your child exhibits certain behaviors and explain that if they respond to those behaviors at all they are actually reinforcing them. If they are incapable of doing that I would limit my child's exposure to them... don't have them over for dinner, but take them with you when you go to the park (where hopefully your child will be so busy that throwing fits will never be an issue). I think it is completely ridiculous and immature of your in-laws to call your child names - when has name calling ever helped a child? My husband used to be defensive about his parents also and that is a tough situation. The best thing that I ever did was to let me husband take the kids to see the in-laws alone and let him deal with any situations that arose. He became more aware of his parent's shortcomings, and became a better parent around his parents each time that situation occurred. It was hard on me to do that sometimes because my imagination ran wild about all of the bad things that could happen to my kids, but nothing bad really happened and my husband became much more engaged and aware when he had to deal with parenting on his own.